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Since its introduction, exploring the situations of extreme agreement and disagreement under different circumstances has been a subject of interest, in order to achieve a better understanding of this index. Here, an explicit formula for the lowest possible value of the ARI for two clusterings of given sizes is shown, and moreover a specific pair of clusterings achieving such a bound is provided.<\/jats:p>","DOI":"10.1007\/s11634-022-00491-w","type":"journal-article","created":{"date-parts":[[2022,2,9]],"date-time":"2022-02-09T11:04:51Z","timestamp":1644404691000},"page":"125-133","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":70,"title":["Minimum adjusted Rand index for two clusterings of a given size"],"prefix":"10.1007","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3675-1960","authenticated-orcid":false,"given":"Jos\u00e9 E.","family":"Chac\u00f3n","sequence":"first","affiliation":[]},{"given":"Ana I.","family":"Rastrojo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,2,9]]},"reference":[{"key":"491_CR1","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/s00357-006-0017-z","volume":"23","author":"AN Albatineh","year":"2006","unstructured":"Albatineh AN, Niewiadomska-Bugaj M, Mihalko D (2006) On similarity indices and correction for chance agreement. 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